Neural Network Inference Method And Its Application Based On Multi-dimensional Hawkes Process Likelihood Ratio

Neuroscientific research has shown that the spikes released by neurons are the basic units for information transmission between neurons.Inferring neuronal networks based on the spike sequence can simulate the information processing of neurons,and the structure of neuronal networks is closely related to cognitive function.Therefore,inferring neuronal networks has great potential in studying cognitive dysfunction related to neurodegenerative diseases.Currently,existing methods for inferring neuronal networks and their application in neurodegenerative diseases have made some progress.However,there are still some shortcomings:(1)Traditional multidimensional Hawkes processes are difficult to judge whether the effective connections between neurons are due to bias in parameter estimation,which can lead to erroneous inference;(2)Previous studies have found that the topology of neuronal networks has an important impact on cognitive function,but there is insufficient understanding of the relationship between the topology of neuronal networks in Down syndrome patients and memory impairments.To address these issues,this paper proposes a method for inferring neuronal networks based on multidimensional Hawkes process likelihood ratio and applies it to the HPC-PFC circuit of Down syndrome mice.The main content of the paper is summarized as follows:To address the problem that traditional multidimensional Hawkes processes are difficult to accurately infer neuronal networks,this paper proposes a method for inferring neuronal networks based on the multidimensional Hawkes process likelihood ratio.Firstly,the multidimensional Hawkes process is used to describe the multidimensional neuronal spike sequence,and the likelihood function is constructed and solved.Then,the likelihood ratio statistic of the multidimensional Hawkes process is proposed,and the significance of Granger causality is tested using multiple hypothesis testing methods to infer the effective connections between neurons and obtain the neuronal network.Simulation experiments show that the proposed method performs best in comprehensive performance compared with the current popular three Granger causality inference methods: transfer entropy,standard multidimensional Hawkes processes,and generalized linear model GC methods.The average recall rate is improved by 82% compared to transfer entropy,94% compared to generalized linear model GC methods,and is comparable to standard multidimensional Hawkes processes.The average false alarm rate is reduced by 29% compared to standard multidimensional Hawkes processes and 3% compared to generalized linear model GC methods,and is comparable to transfer entropy.To address the lack of understanding of the relationship between the topology of neuronal networks in Down syndrome patients and memory impairments in previous studies,this paper applies the proposed method to infer the neuronal networks of the HPCPFC circuit in Down syndrome mice and their control group.Through complex network analysis,it is found that the adaptability reorganization trend of the neuronal network topology in the HPC-PFC circuit of Down syndrome mice is abnormal.Specifically,when responding to the demand of memory discrimination,there is no increasing trend of crossregional connections from HPC to PFC that reflect memory loading processes,and there is no increasing trend of PFC neuronal network clustering coefficient during memory discrimination.The HPC-PFC circuit neuronal network of Down syndrome mice exhibits excessively high modularity during wakeful rest and novel object recognition states,indicating abnormal cognitive processes during memory consolidation and memory discrimination stages.These findings provide new insights and theoretical basis for the study of neurophysiological factors in Down syndrome memory impairments.